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Largest Set Rule for ALB via Bi-Directional Work Relatedness

Paper:

Enhancing the Largest Set Rule for Assembly Line BalancingThrough the Concept of Bi-Directional Work Relatedness

Konstantinos N. Genikomsakis and Vassilios D. Tourassis

Department of Production Engineering and Management, School of Engineering, Democritus University of Thrace

GR-67100, Kimmeria, Xanthi, Greece

Email: {kgenikom, vtourasi}@pme.duth.gr

[Received September 16, 2009; accepted January 21, 2010]

The process of optimally assigning the timed tasks re-

quired to assemble a product to an ordered sequence

of workstations is known as the Assembly Line Bal-

ancing (ALB) problem. Typical approaches to ALB

assume a strict mathematical posture and mostly treat

it as a combinatorial optimization problem with the

objective of minimizing the idle time across the work-

stations, while satisfying precedence constraints. The

actual nature of the tasks assigned is seldom taken into

consideration. While this approach may yield satis-

factory cycle time results on paper, it often leads to

inconvenient task assignments in an actual work envi-

ronment. It has been postulated in the literature that

assigning groups of related tasks to the same worksta-

tion may lead to assembly lines that exhibit increased

robustness in real-world situations at the expense of a

slightly increased cycle time. The prototypical exam-

ple of such an approach, Agrawals Largest Set Rule

(LSR), utilizes backward work relatedness to assigna set of cohesive tasks to the proper workstation. In

this paper, we enhance the performance of the original

LSR algorithm through the concept of bi-directional

work relatedness, where backward and forward rela-

tionships are taken into consideration for task assign-

ments. The proposed concept leads to comparable cy-

cle time and improved work relatedness. Applying this

novel concept to a benchmark ALB problem demon-

strates the feasibility and applicability of the proposed

approach.

Keywords: assembly line balancing, work relatedness

1. Introduction

Assembly lines are high volume production systems

that operate based on the principle of division of labour.

The process of assigning the work elements that com-

pose the production process to individual workstations

is known as the Assembly Line Balancing (ALB) prob-

lem. The strategic role of the ALB problem on overall

business performance is well recognized [1] and its solu-

tion has attracted significant research effort over the pastdecades [2].

There are two dual representations of the ideal Sim-

ple Assembly Line Balancing (SALB) problem: if the de-

sired cycle time is given, minimize the number of work-

stations needed (SALB-I) or if the number of workstations

is given, maximize the actual production rate (SALB-II).

Assigning Ntasks to m workstations is an NP-hard

combinatorial optimization problem and employing typ-

ical mathematical tools for solving real world industrial

problems is prohibitive. As a consequence, numerous

heuristic tools for providing ALB solutions have been de-

velopedbut few have been put into real-world use [3]. The

reason for the limited practicality of these approaches is

that they treat the ALB problem mostly as a mathemati-

cal problem, consisting of a set of constraints that must be

satisfied and one or more objectives that should be opti-

mized [4]. The actual nature of the tasks assigned is sel-

dom taken into consideration. While this approach may

yield satisfactory cycle time results on paper, it often leads

to inconvenient task assignments in an actual work envi-ronment. The fact that the research efforts were mainly

focused on optimality, and rather less attention has been

paid to the practicality of the solutions [5], has contributed

to this divergence between the academic ALB approach

and todays industry needs [6]. To bridge this gap, in the

seminal review paper of [2] it is advocated that research

efforts should be directed to generalizations of the clas-

sical ALB problem that examine it under more realistic

conditions.

It has been postulated in the literature that assigning

groups of related tasks to the same workstation may lead

to assembly lines that exhibit increased robustness in real-world situations at the expense of a slightly increased

cycle time. The prototypical example of such an ap-

proach, Agrawals Largest Set Rule (LSR), utilizes back-

ward work relatedness to assign a set of cohesive tasks

to the proper workstation [4] (while Agrawals LSR ap-

proach dates back to the late eighties, it remains current

to this date and it is the only priority rule-based algorithm

for work relatedness). The aim of this paper is twofold:

to highlight the practical importance of the concept of re-

lated activities, which is mostly ignored in typical ALB

approaches, and to propose an extension of Agrawals

Largest Set Rule for improving the work relatedness of

the tasks assigned to workstations.In this context, we enhance the performance of the orig-

Vol.14 No.4, 2010 Journal of Advanced Computational Intelligence 353

and Intelligent Informatics

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Genikomsakis, K. N. and Tourassis, V. D.

inal LSR algorithm through the concept of bi-directional

work relatedness, where backward andforward relation-

ships are taken into consideration for task assignments.

The results obtained by the proposed solution procedure

are compared in terms of optimality and practicality with

both the original Largest Set Rule and the optimal ones

that can be obtained through any enumerative ALB pro-

cedure. Our analysis reveals that the compromise betweenoptimality and practicality provides desirable advantages.

2. Mathematical Model for SALB-I

Let Nbe the number of tasks of the assembly process

and maxWS be the upper bound on the number of work-

stations. The time required to perform taski is denoted

by ti and the available time for completing the tasks as-

signed to a workstation, namely the cycle time, is denoted

by CT. PR denotes the set of task pairs (g,h) that repre-sent precedence relations between tasks g and h (taskg is

an immediate predecessor of taskh), while decision vari-

ables xikare equal to 1 if taski is assigned to workstation

k; otherwise 0.

The problem of minimizing the number of the work-

stations for a given cycle time CTis formulated as fol-

lows [7]:

Minimize: z=maxWS

k=1

k xik . . . . . . . . (1)

subject to the constraints:

maxWS

k=1 xik= 1 i {1, . . . ,

N} . . . . . . . (2)

maxWS

k=1

k xgkmaxWS

k=1

k xhk(g,h) PR . . . (3)

N

i=1

ti xikCTk {1, . . . , maxWS} . . . . (4)

xik {0, 1}i {1, . . . ,N}, k {1, . . . , maxWS} (5)

The objective function in Eq. (1) minimizes the num-

ber of workstations of the ALB solution. The set of con-

straints in Eq. (2) ensure that every task is assigned to ex-actly one workstation, while restrictions in Eq. (3) guar-

antee that the task precedence relationships are satisfied

(a taskh cannot be assigned to a workstation prior to its

predecessor g). Constraints in Eq. (4) enforce the work-

load of each workstation not to exceed the cycle time CT

and the decision variables in Eq. (5) are denoted as binary.

3. The Concept of Related Activities

Typically ALB problems are represented with a prece-

dence diagram, where the tasks and the precedence rela-

tions between them are depicted as nodes and arcs respec-tively. Besides imposing restrictions to the order in which

Fig. 1. Precedence diagram of the Jackson problem.

the tasks can be assigned to workstations, precedence re-

lations of the form (g,h) can serve as an indicator of re-latedness between them according to [4]. This approach,

although imperfect, is based on the premise that the work

elements related to a specific subassembly will have more

precedence relations within themselves rather than with

tasks related to other subassemblies. For instance, Fig. 1

depicts the precedence diagram of the well-known bench-mark Jackson problem. In this case, tasks 3, 4, 5 and 9

are considered more related to task 7 compared to task 2,

whereas the latter task along with tasks 1, 3, 4, and 5 form

a set of coherent tasks.

Assigning related tasks to workstations provides sev-

eral advantages that cannot be directly assessed via ex-

isting assembly line balancing measures such as line ef-

ficiency, balance efficiency or smoothness index. Indica-

tively, this task assignment approach [4, 8, 9]:

is expected to mitigate phenomena, like low job sat-

isfaction and lack of motivation, that have been con-

nected to the execution of repetitive tasks in assem-bly lines that involve manual labor [10],

facilitates the identification of the causes of defects

on the product or the production process due to the

reduced number of workers engaged to specific sub-

assemblies,

moderates the repercussions to a lower number of

workstations when changes on the production pro-

cess or the product are made, as they are likely to

affect specific subassemblies that are represented as

a group of related tasks on the precedence diagram,

offers greater flexibility during the design phase, asthe designer is given more options to arrange the

workstations along the assembly line.

The improved supervision of the assembly process, the

flexible design and the more efficient operation of the pro-

duction system however do come at a cost. It is evident

that assigning only related work elements to workstations

is likely to produce solutions with higher cycle time for

a given number of workstations, but a reasonable com-

promise between the practicality of the solution and the

achieved cycle time may prove to be beneficial.

A measure of work relatedness was proposed in [8]

based on Agrawals concept of related activities. Specifi-

cally, the Index of Work Relatedness (IWR) quantifies the

354 Journal of Advanced Computational Intelligence Vol.14 No.4, 2010

and Intelligent Informatics